Whitening filter and innovations representation of self-similar process. (Q1419035)

Different representations of fractional Brownian motion are proposed as \(B^H_t= \int K^H(t,s)\,dB_s\) with different kernels \(K^H\) and a standard Brownian motion \(B\). Reciprocally, \(B\) is written as an integral with respect to Liouville fractional Brownian motion \(B^H_0\) depending on \(H\in ]0,{1\over 2}[\) or \(H\in ]{1\over 2},1[\).